Geometric theory of functions of a complex variable:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Society
1969
|
| Series: | Translations of Mathematical Monographs
26 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russischen übersetzt - Literaturverzeichnis Seiten 651 - 672 |
| Physical Description: | VI, 676 Seiten graph. Darst. |
Staff View
MARC
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| 100 | 1 | |a Goluzin, G.M. |d 1906-1952 |e Verfasser |0 (DE-588)108982338X |4 aut | |
| 240 | 1 | 0 | |a Geometričeskaja teorija funkcij kompleksnogo peremennogo |
| 245 | 1 | 0 | |a Geometric theory of functions of a complex variable |c by G. M. Goluzin |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 1969 | |
| 300 | |a VI, 676 Seiten |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Translations of Mathematical Monographs |v 26 | |
| 500 | |a Aus dem Russischen übersetzt - Literaturverzeichnis Seiten 651 - 672 | ||
| 650 | 7 | |a analyse harmonique convergence |2 inriac | |
| 650 | 7 | |a fonction variable complexe |2 inriac | |
| 650 | 7 | |a problème valeur limite |2 inriac | |
| 650 | 7 | |a représentation conforme |2 inriac | |
| 650 | 7 | |a théorie géométrique |2 inriac | |
| 650 | 0 | 7 | |a Komplexe Variable |0 (DE-588)4164905-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Funktionentheorie |0 (DE-588)4018935-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Geometrische Funktionentheorie |0 (DE-588)4156711-0 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804120470683910144 |
|---|---|
| adam_text | TABLE OF CONTENTS
Page
A note on the author 1
Preface to the second edition 3
Preface (to the first edition) 4
Introductory geometric considerations 5
Chapter I. The convergence of sequences of analytic and harmonic
functions 11
§1. The convergence of sequences of analytic functions 11
§2. The condensation principle 14
§3 The convergence of sequences of harmonic functions 19
Chapter II. The principles of conformal mappings of simply connected
domains 23
§1. Univalent conformal mapping 23
§2. Riemann s theorem 25
§3 The correspondence of boundaries under conformal mapping 31
§4. Distortion theorems 47
§5 Convergence theorems on the conformal mapping of a sequence
of domains 54
§6. Modular and automorphic functions 62
§7. Normal families of analytic functions. Applications 67
Chapter III. Realization of conformal mapping of simply connected
domains 76
§1. Conformal mapping of domains bounded by rectilinear and
circular polygons 76
§2. Parametric representation of univalent functions 89
§3. Variation of univalent functions 99
Chapter IV. Extremal questions and inequalities holding in classes of
univalent functions 110
§1. Rotation theorems 110
§2. Sharpening of the distortion theorems 118
iii
iv
§3. Extrema and majorizations of the type of the distortion theorems 128
§4. Application of the method of variations to other extremal
problems 140
§5. Limits of convexity and starlikeness 165
§6. Covering of segments and areas 170
§7. Lemmas on the mean modulus. Bounds for the coefficients 182
§8. The relative growth of coefficients of univalent functions 190
§9. Sharp bounds on the coefficients 196
Chapter V. Univalent conformal mapping of multiply connected domains 205
§1. Univalent conformal mapping of a doubly connected domain onto
an annulus 205
§2. Univalent mapping of a multiply connected domain onto a plane
with parallel rectilinear cuts 210
§3. Univalent mapping of a multiply connected domain onto a helical
domain 216
¦§4. Some relationships involving the mapping functions 222
§5 Convergence theorems for univalent mapping of a sequence of
domains 228
§6. Univalent mapping of multiply connected domains onto circular
domains. The continuity method 234
§7. Proof of Brouwer s theorem 244
Chapter VI. Mapping of multiply connected domains onto a disk 254
§1. Conformal mapping of a multiply connected domain onto a disk 254
§2. Correspondence of boundaries under a mapping of a multiply
connected domain onto a disk 262
§3 Dirichlet s problem and Green s function 266
§4. Application to a univalent mapping of multiply connected domains ....275
§5. Mapping of an n connected domain onto an n sheeted disk 277
§6. Some identities connecting a univalent conformal mapping and
the Dirichlet problem 283
Chapter VII. The measure properties of closed sets in the plane 293
§1. The transfinite diameter and Cebysev s constant 293
§2. Bounds for the transfinite diameter 300
§3. The capacity of a closed bounded set 309
§4. Harmonic measure of closed bounded sets 314
§5. An application to meromorphic functions of bounded form 321
V
Chapter VIII. Majorization principles and their applications 329
§1. An invariant form of the Schwarz lemma 329
§2. The hyperbolic metric principle 336
§3 Lindelof s principle 339
§4. Harmonic measure. The simplest applications 341
§5 On the number of asymptotic values of entire functions of finite
order 351
§6. The hyperconvergence of power series 356
§7. A nonanalytic generalization of the Schwarz lemma. A theorem
on covering of disks 360
§8. Majorization of subordinate analytic functions 368
Chapter IX. Boundary value problems for analytic functions defined on a
disk 380
§1. Limiting values of Poisson s integral 380
§2. The representation of harmonic functions by means of Poisson s
integral and the Poisson Stieltjes integral 385
§3 The limiting values of analytic functions 393
§4. Boundary properties of functions in the class H 402
§5. Functions that are continuous on a closed disk 409
Chapter X. Boundary questions for functions that are analytic inside a
rectifiable contour 417
§1. The correspondence of boundaries under conformal mapping 417
§2. Privalov s uniqueness theorem 428
§3 On the limiting values of Cauchy s integral 430
§4. Cauchy s formula 435
§5 Classes of functions. Cauchy s formula 438
§6. On the extrema of mean moduli 441
§7. Approximation in mean and the theory of orthogonal polynomials 448
Chapter XI. Some supplementary information 454
§1. Gluing theorems 454
§2. Conformal mapping of simply connected Riemann surfaces 461
§3 An extremum for bounded functions in multiply connected domains .... 467
§4. The three disk theorem 476
§5. Transformation of analytic functions by means of polynomials 480
§6. On p valent functions ; 487
vi
§7. Some remarks on the Caratheodory Fejer problem and on an
analogous problem 497
§8. Some inequalities for bounded functions 514
§9 A method of variations in the theory of analytic functions 526
The scientific works of Gennadit Mihatlovic Goluzin 545
Bibliography 549
Supplement. Methods and results of the geometric theory of functions 563
Introduction 563
§1. Basic methods of the geometric theory of functions of a complex
variable 565
§2. Univalent functions in a disk and in an annulus 577
§3. Functions that are analytic in multiply connected domains 629
Bibliography for the Supplement 651
Subject Index 673
|
| any_adam_object | 1 |
| author | Goluzin, G.M. 1906-1952 |
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| bvnumber | BV006256473 |
| classification_rvk | SK 750 SK 700 |
| ctrlnum | (OCoLC)493608844 (DE-599)BVBBV006256473 |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T16:42:36Z |
| institution | BVB |
| language | English |
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| physical | VI, 676 Seiten graph. Darst. |
| publishDate | 1969 |
| publishDateSearch | 1969 |
| publishDateSort | 1969 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Translations of Mathematical Monographs |
| series2 | Translations of Mathematical Monographs |
| spelling | Goluzin, G.M. 1906-1952 Verfasser (DE-588)108982338X aut Geometričeskaja teorija funkcij kompleksnogo peremennogo Geometric theory of functions of a complex variable by G. M. Goluzin Providence, RI American Mathematical Society 1969 VI, 676 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Translations of Mathematical Monographs 26 Aus dem Russischen übersetzt - Literaturverzeichnis Seiten 651 - 672 analyse harmonique convergence inriac fonction variable complexe inriac problème valeur limite inriac représentation conforme inriac théorie géométrique inriac Komplexe Variable (DE-588)4164905-9 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Geometrische Funktionentheorie (DE-588)4156711-0 gnd rswk-swf Komplexe Variable (DE-588)4164905-9 s Funktionentheorie (DE-588)4018935-1 s DE-604 Geometrische Funktionentheorie (DE-588)4156711-0 s 1\p DE-604 Translations of Mathematical Monographs 26 (DE-604)BV000002394 26 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003951508&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Goluzin, G.M. 1906-1952 Geometric theory of functions of a complex variable Translations of Mathematical Monographs analyse harmonique convergence inriac fonction variable complexe inriac problème valeur limite inriac représentation conforme inriac théorie géométrique inriac Komplexe Variable (DE-588)4164905-9 gnd Funktionentheorie (DE-588)4018935-1 gnd Geometrische Funktionentheorie (DE-588)4156711-0 gnd |
| subject_GND | (DE-588)4164905-9 (DE-588)4018935-1 (DE-588)4156711-0 |
| title | Geometric theory of functions of a complex variable |
| title_alt | Geometričeskaja teorija funkcij kompleksnogo peremennogo |
| title_auth | Geometric theory of functions of a complex variable |
| title_exact_search | Geometric theory of functions of a complex variable |
| title_full | Geometric theory of functions of a complex variable by G. M. Goluzin |
| title_fullStr | Geometric theory of functions of a complex variable by G. M. Goluzin |
| title_full_unstemmed | Geometric theory of functions of a complex variable by G. M. Goluzin |
| title_short | Geometric theory of functions of a complex variable |
| title_sort | geometric theory of functions of a complex variable |
| topic | analyse harmonique convergence inriac fonction variable complexe inriac problème valeur limite inriac représentation conforme inriac théorie géométrique inriac Komplexe Variable (DE-588)4164905-9 gnd Funktionentheorie (DE-588)4018935-1 gnd Geometrische Funktionentheorie (DE-588)4156711-0 gnd |
| topic_facet | analyse harmonique convergence fonction variable complexe problème valeur limite représentation conforme théorie géométrique Komplexe Variable Funktionentheorie Geometrische Funktionentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003951508&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
| work_keys_str_mv | AT goluzingm geometriceskajateorijafunkcijkompleksnogoperemennogo AT goluzingm geometrictheoryoffunctionsofacomplexvariable |